What is coordinate geometry? Well, it is about the plotting of graphs and points on a graph, which consists of the x-axis (horizontal line) and the y-axis (vertical line).
Equation of a Line: y = mx + c
These are the 3 formulas that are needed to be learnt:
What is m? m refers to the gradient of a line which can be calculated through the gradient formula as stated above. Thus, m will define the number of variables of x. The value of m determines the slope of the line, the greater the value of m, the steeper the line, when m = 0, it produces a horizontal line.
What is c? c refers to the y-intercept which can be easily seen or calculated through the graph. To put it simply, c is the point where the line intersects on the y-axis.
So, is there anything besides that? No, actually in coordinate geometry. After you manage to decipher what m and c is respectively, you are able to draw out a graph. However, do note that you are still able to draw a graph even without knowing the variables. How can coordinate geometry be tested? It can be tested in any form. Usually, questions can give you figures and you need to make use of the 3 important formulas to solve the question.
Lesson 2: Simultaneous Linear Equations
There are actually the 2 most common methods to solve simultaneous linear equations, which are elimination and substitution.
In elimination, we usually try to make one of the variables the same in both equations, then we will subtract or add them, resulting in an equation only having the other variable and the number or product. Then we solve for this variable, before substituting it in to the any other equation to solve for the other variable.
In substitution, we usually try to get how much of variable 1 equals to how much of variable 2 (e.g. x = 2y). How do we do it, we usually make the number of product the same first and form an equation with only the 2 variables. Then, we get the most important equation, as stated in the first sentence. Then, we will substitute one of the variables which mean we get the same product for elimination and in the end, substitute the value of the variable into the equation to solve for the other variable.
I personally feel that elimination will be a better way because it is much faster though lengthier, there needs to be a lot of steps. However, it is more systematic and does not confuse you. Substitution is good when solving complicated equations, but not needed when solving simple equations.
Actually, there is a last way but is used rarely during tests. So, there are actually 3 answers to questions when doing simultaneous linear equations:
1.) Unique (Only a Few Specific Answers) 2.) Many/Infinite Solutions 3.) No Solution
The last method is actually a graph and what happens under the different circumstances.
When there is a unique solution, there is an intersection point between the 2 lines, when there are many infinite solutions, the two equations are on the same line, having infinite points of intersection while when there is no solution, the two lines are parallel and will never intersect.
Lesson 3: Trigonometry
In trigonometry this term, we have not learnt that much but we learnt the basics of trigonometry, only involving right-angled triangles. What are the three sides of a right-angled triangle?
1.) Hypotenuse – Side opposite the Right Angle 2.) Adjacent – Side touching the Required Angle 3.) Opposite – Side not touching the Required Angle
There are basically 3 trigonometric functions to remember and its reciprocals:
There are some other formulas that could be learnt, showing us the comparison between the 3 trigonometric functions:
1.) cosec theta = 1/sin theta 2.) sec theta = 1/cos theta 3.) cot theta = 1/ tan theta 4.) sin theta = cos (90 degrees – theta) 5.) cos theta = sin (90 degrees – theta) 6.) tan theta = cot (90 degrees – theta
Besides, we have also learnt about elevation and depression.
Angle of Elevation: Angle between the horizontal line from object to sight and line from sight to top of object
Angle of Depression: Angle between the horizontal line of top of sight and line between the top of the sight and object
So, what is there to solve in trigonometry? We have to make use of the different formulas such as to solve for specific angles.
Lesson 1: Coordinate Geometry
What is coordinate geometry? Well, it is about the plotting of graphs and points on a graph, which consists of the x-axis (horizontal line) and the y-axis (vertical line).
Equation of a Line: y = mx + c
These are the 3 formulas that are needed to be learnt:
1.) Gradient: y2 – y 1 / x2 – x1
2.) Distance Formula: Square Root {(x2 – x1) ^2 + (y2 – y1) ^2} (Makes use of Pythagoras Theorem)
3.) Midpoint Formula: x1 + x2 / 2, y1 + y2 / 2
What is m? m refers to the gradient of a line which can be calculated through the gradient formula as stated above. Thus, m will define the number of variables of x. The value of m determines the slope of the line, the greater the value of m, the steeper the line, when m = 0, it produces a horizontal line.
What is c? c refers to the y-intercept which can be easily seen or calculated through the graph. To put it simply, c is the point where the line intersects on the y-axis.
So, is there anything besides that? No, actually in coordinate geometry. After you manage to decipher what m and c is respectively, you are able to draw out a graph. However, do note that you are still able to draw a graph even without knowing the variables. How can coordinate geometry be tested? It can be tested in any form. Usually, questions can give you figures and you need to make use of the 3 important formulas to solve the question.
Lesson 2: Simultaneous Linear Equations
There are actually the 2 most common methods to solve simultaneous linear equations, which are elimination and substitution.
In elimination, we usually try to make one of the variables the same in both equations, then we will subtract or add them, resulting in an equation only having the other variable and the number or product. Then we solve for this variable, before substituting it in to the any other equation to solve for the other variable.
In substitution, we usually try to get how much of variable 1 equals to how much of variable 2 (e.g. x = 2y). How do we do it, we usually make the number of product the same first and form an equation with only the 2 variables. Then, we get the most important equation, as stated in the first sentence. Then, we will substitute one of the variables which mean we get the same product for elimination and in the end, substitute the value of the variable into the equation to solve for the other variable.
I personally feel that elimination will be a better way because it is much faster though lengthier, there needs to be a lot of steps. However, it is more systematic and does not confuse you. Substitution is good when solving complicated equations, but not needed when solving simple equations.
Actually, there is a last way but is used rarely during tests. So, there are actually 3 answers to questions when doing simultaneous linear equations:
1.) Unique (Only a Few Specific Answers)
2.) Many/Infinite Solutions
3.) No Solution
The last method is actually a graph and what happens under the different circumstances.
When there is a unique solution, there is an intersection point between the 2 lines, when there are many infinite solutions, the two equations are on the same line, having infinite points of intersection while when there is no solution, the two lines are parallel and will never intersect.
Lesson 3: Trigonometry
In trigonometry this term, we have not learnt that much but we learnt the basics of trigonometry, only involving right-angled triangles. What are the three sides of a right-angled triangle?
1.) Hypotenuse – Side opposite the Right Angle
2.) Adjacent – Side touching the Required Angle
3.) Opposite – Side not touching the Required Angle
There are basically 3 trigonometric functions to remember and its reciprocals:
1.) Sine = Opposite/Hypotenuse (Cosecant)
2.) Cosine =Adjacent/Hypotenuse (Secant)
3.) Tangent = Opposite/Adjacent (Cotangent)
There are some other formulas that could be learnt, showing us the comparison between the 3 trigonometric functions:
1.) cosec theta = 1/sin theta
2.) sec theta = 1/cos theta
3.) cot theta = 1/ tan theta
4.) sin theta = cos (90 degrees – theta)
5.) cos theta = sin (90 degrees – theta)
6.) tan theta = cot (90 degrees – theta
Besides, we have also learnt about elevation and depression.
Angle of Elevation: Angle between the horizontal line from object to sight and line from sight to top of object
Angle of Depression: Angle between the horizontal line of top of sight and line between the top of the sight and object
So, what is there to solve in trigonometry? We have to make use of the different formulas such as to solve for specific angles.
Sin degrees: 30= 1/2 45= 1/square root 2 60= square root 3/2 9 = 1
Cosine degrees: 30 = square root 3/2 45= 1/square root 2 60=1/2 90=0
Tangent degrees: 30=1/square root 3 45=1 60=square root 3 90=undefined